A multiregion discrete-time epidemic model of \textit{Mycobacterium tuberculosis} infections: an optimal control approach
type: Item
instance of: scholarly article
title: A multiregion discrete-time epidemic model of \textit{Mycobacterium tuberculosis} infections: an optimal control approach
zbMATH Open document ID: 1471.92292
DOI: 10.1155/2021/5594778
author: Rachid Bouajaji
author: Hassan Laarabi
author: Mostafa Rachik
author: Abdelhadi Abta
published in: Discrete Dynamics in Nature and Society
publication date: 2021-08-12T00:00:00Z
review text: Summary: The main goal of this article is to devise the spatial-temporal spread of TB, in multiple neighboring domains, taking into account the epidemiological diversity of their populations. However, since both the environment and any population are spatially heterogeneous, it is obviously desirable to include spatial structure into an epidemic model. Individuals with tuberculosis can spread the disease by moving from one area to another. In addition, people travel by air between cities, so diseases can be spread quickly between very distant places (as was the case with the COVID-19). In our model, each region's studied population is divided into five compartments \(\mathrm{S}\), \(\mathrm{L}_1\), \(\mathrm{I}\), \(\mathrm{L}_2\), and \(\mathrm{R}\). Further, we introduce in our discrete systems three control variables which represent the effectiveness rates of vaccination, travel-blocking operation, and treatment. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added, we finish with the introduction of the treatment control. The optimal control theory, based on Pontryagin's maximum principle, is applied thrice in this paper, for the characterizations of the vaccination, travel-blocking, and treatment controls. The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge-Kutta fourth-order schemes.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 7381280
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5594778
OpenAlex ID: W3170633329
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description: scientific article; zbMATH DE number 7381280